Computational Water, Energy, and Environmental Engineering, 2015, 4, 25-37
Published Online July 2015 in SciRes. http://www.scirp.org/journal/cweee
http://dx.doi.org/10.4236/cweee.2015.43004
Modeling of Discharge Distribution in Bend
of Ganga River at Varanasi
Manvendra Singh Chauhan*, Prabhat Kumar Singh Dikshit, Shyam Bihari Dwivedi
Department of Civil Engineering, Indian Institute of Technology, IIT (BHU), Varanasi, India
Email: *[email protected]
Received 1 May 2015; accepted 6 June 2015; published 9 June 2015
Copyright © 2015 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Abstract
Dynamics of river behavior play a great role in meandering, sediment transporting, scouring, etc.
of river at bend, which solely depends on hydraulics properties such as horizontal and vertical
stress, spatial and temporal variation of discharge. Therefore understanding of discharge distribution of river Ganga is essential to apprehend the behavior of river cross section at bend particularly. The measurement of discharge is not very simple as there is no instrument that can measure the discharge directly, but velocity measurement at a section can be made. Velocity distribution at different cross sections at a time is also not easy with single measurement with the help of
any instrument and method, so it required repetitions of the measurement. Velocity near the end
of bank, top and bottom layer of natural streams is difficult to be measured, yet velocity distribution at these regions plays important role in characterizing the behavior of river. This paper deals
with the new advanced discharge measurement technique and measured discharge data has been
used for modelling at river bend. To carry out the distribution of discharge and velocity with
depth in river Ganga, the length of river in study area was distributed into 14 different cross sections, M-1 to M-14, measured downstream to upstream and the measurement was done by using of
ADCP (Acoustic Doppler Current Profiler). At each cross section, profiles were measured independently by an ADCP and data acquired from ADCP were further used for the regression modeling. A multiple linear regression model was developed, which showed a high correlation among
the discharge, depth and velocity parameters with the root mean square error (R2) value of 0.8624.
Keywords
ADCP, Discharge, Linear Regression, River, RMS
1. Introduction
Flow in open channel and a natural river is often described by simplifying cross section. But in reality cross sec*
Corresponding author.
How to cite this paper: Chauhan, M.S., Dikshit, P.K.S. and Dwivedi, S.B. (2015) Modeling of Discharge Distribution in Bend
of Ganga River at Varanasi. Computational Water, Energy, and Environmental Engineering, 4, 25-37.
http://dx.doi.org/10.4236/cweee.2015.43004
M. S. Chauhan et al.
tion of river and its bend is so complicated that it needs vast practical experience to understand the hydrodynamics. On the other hand the most dangerous natural disaster, worldwide known as flood, can cause a huge
economic losses as well as losses of life and livelihood. Therefore understanding the flow behavior and estimation of discharge for open channel flow (most commonly natural rivers) is very vital hence it had keen interest
for the researchers for decades. Many researchers develop various methods for the discharge estimation; however, some enhance the accuracy of the previously available methods. Researcher develops regression based models [1]-[3] and some develop soft computing methods [4]-[6]. The main river flow (discharge of river) might be
changed at a very large scale as human interruption takes place in term of occupying the place along the river
bank or within the river basin [7]. Regression based approach is most commonly very useful for the ungauged
sites for discharge estimation [8]-[10].
The increase in the flow of any river is caused by the large volume of rainfall in its basin, which would probably change the physical parameters of the river involving the changes in the depth due to bank erosion’ taking
place and width of flow [11]-[14]. The river hydrodynamics could directly affect the flow pattern of river and may
change in river morphology. [15]-[18] observed that the meandering is one of the most common pattern followed by fluvial rivers. A lot of research work is completed by researchers for the study of bankfull discharge
and bankfull velocity of river, but there is a lack of research about the natural flow and natural velocity of river.
It is to understand that, the discharge of river is a function of river meandering wavelength and amplitude, as
the higher the value of river meandering wavelength and amplitude, higher will be the discharge and vice versa.
The above understanding gives a way to go forward with this research in the direction that the river parameters
must naturally have a relationship with each other. The main purpose of this paper is to develop a correlation
among parameters of Varanasi bend of holy River Ganga which are directly related to the physical parameters of
river i.e. discharge, depth and velocity. The complete measurement on the Varanasi bend was done in the month
of November 2013.
With the progresses of measuring discharge and understanding behavior of Natural River, Acoustic Doppler
Current Profiler (ADCP) technologies, a moving boat discharge measurement technique is gradually replacing
the classic procedure using mechanical meters when the water is sufficiently deep for ADCP applications. While
measuring discharge through ADCP, the transducers of an ADCP are mounted facing down and barely submerged under the water surface. They ping continuously while the boat is traversing from bank to bank. The
boat motion is monitored by bottom tracking acoustic pings or by a global positioning system (GPS). The water
flux crossing the vertical plane of the boat path is computed, which is the same as the river discharge. The
ADCP can be used for measuring a velocity profile in the vertical when the ADCP is held at a fixed position for
taking a large number of the single ping velocity measurements. The averaged single ping velocity profiles reduce the measurement errors so that a meaningful mean velocity profile can be obtained.
This paper is designed to address the following objectives by using data generated from the ADCP
 Quantify the discharge and velocity distribution for the different cross section along the bend of river Ganga
 Identify relationships between different hydraulic parameters and thus perform regression analysis.
Organization of paper includes:
 an overview of the discharge measurement and regression modeling
 description of study area (Section 2)
 descriptions of the methods used (Section 3)
 the data analysis and model development (Section 4)
 discussion of the results (Section 5); and
 conclusions (Section 6).
2. Study Area
Varanasi (25˚20'N and 83˚7'E) is located in the middle Ganges valley of North India, in the Eastern part of the
Uttar Pradesh, along the left crescent-shaped bank of the Ganges, averaging between 50 feet (15 m) and 70 feet
(21 m) above the river. It is oldest city situated on the convex bank of holy River Gangaas shown in Figure 1. It
is called the longest river of India, having its total length 2525 KM from Gangotri to Ganga Sagar. Being located
in the Indo-Gangetic Plains of North India, the land is very fertile because low level floods in the Ganges continually replenish the soil. Varanasi is often said to be located between two confluences: one of the Ganges and
Varuna, and other of the Ganges and Assi, although the latter has always been a rivulet rather than a river. The
26
M. S. Chauhan et al.
Figure 1. Study area: natural bend in river Ganga at varanasi.
distance between the two confluences is around 2.5 miles (4.0 km). Rarely has any river gathered in itself so
much meaning and reverence as the Ganga has over three millennia in the Indian subcontinent. The land-water
interface on the Ganga’s banks is fashioned out of the need to access the rising and falling water levels in the
monsoon and dry seasons. The cultural landscape of this interface a ghat (steps and landings) lined by temples
and other public buildings, pavilions, kunds (tanks), streets and plazas is layered and kinetic, and responsive to
the river’s flow. At Varanasi, where the Ganga reverses its flow northwards, the ghats describe a crescent sweep
in a 7.6 km stretch.
The climate of the city, as of Northern India on the whole, is of tropical nature with extremes of temperature,
varying from a minimum of 5˚C in winter to a maximum of 45˚C in summer. The annual rainfall varies from
680 mm to 1500 mm, with a large proportion occurring during the monsoon season, in the months of July to
September.
3. Methodology
To achieve the objective of measuring velocity distribution and understanding the behavior of velocity distribution with depth of river in the river cross-section, an ADCP, was used. The whole study river length was divided
into the 14 distinct cross-sections for discharge measurement, named as M-14 to M-1 respectively from upstream of flow to downstream of flow. Further with the help of ADCP, complete profiling for depth and discharge of each cross-section had been done. Recorded ADCP data have been extracted by using the supporting
software of ADCP i.e. Win River-II, for analysis purpose. Excel sheets for each cross-section (from M-1 to
M-14) of distance from bank, velocity and depth was prepared for calibration of regression based model. For
preparation of data, shortest width cross-section was selected and divided it into 4 uniform parts (width wise),
the width of shortest cross-section was 281 meters after dividing it, the division width was 74.25 meters, average
the velocity and depth parameters of each part as V1, V2, V3, V4 & D1, D2, D3, D4 for the cross-section M-7.
The area of each part was also calculated by using AutoCAD software termed as A1, A2, A3, and A4 respectively.
Similarly by applying this process on all the data of each cross-section from M1 to M14 was estimated and
listed in Table 1. M-1 has been divided into 7 parts having the average velocity from V1 to V7, average depth
from D1 to D7 and the area from A1 to A7 and Cross-sectional view with reduced level is also shown in Figure
2, M-2 has been divided into 6 parts having the average velocity from V1 to V6, average depth from D1 to D6
and the area from A1 to A6, M-3 has been divided into 5 parts having the average velocity from V1 to V5,
27
M. S. Chauhan et al.
Table 1. Description of cross sectional data.
Sr. No.
1
2
3
4
5
6
Profile
No.
M-1
M-2
M-3
M-4
M-5
M-6
Total
Width
in (m)
460
434
357
378
386
297
No. of
Division
6.1953
Name of
Average
Depths
Average Depth
in (m)/74.25 m
width
Name of
Average
Velocities
Average
Velocity in
(m)/74.25 m
width
Area of
each divided
section in m2
Discharge
at each
cross section
D1
11.16
V1
0.113
1116.6769
126.18449
D2
19.98
V2
0.221
1475.8199
326.1562
D3
18.11
V3
0.3
1351.3572
405.40716
D4
16.53
V4
0.34
1228.3031
417.62305
D5
11.07
V5
0.34
830.8381
282.48495
D6
6.95
V6
0.14
526.488
73.70832
D7
4.82
V7
0.08
15.2103
1.216824
D1
9
V1
0.192
879.809
168.92333
D2
15.72
V2
0.43
1163.7889
500.42923
D3
14.62
V3
0.371
1094.5191
406.06659
D4
12.98
V4
0.252
967.9261
243.91738
D5
9.7
V5
0.163
731.0454
119.1604
D6
5.58
V6
0.098
210.2677
20.606235
D1
15.44
V1
0.32
1226.6425
392.5256
D2
18.22
V2
0.29
1349.0814
391.23361
D3
14.97
V3
0.3
1112.5433
333.76299
D4
12.86
V4
0.22
950.3806
209.08373
D5
6.8
V5
0.17
391.39
66.5363
D1
15.1
V1
0.173
1271.3793
219.94862
D2
16.31
V2
0.489
1204.4832
588.99228
D3
12.52
V3
0.507
931.5344
472.28794
D4
11.06
V4
0.295
821.6697
242.39256
D5
7.62
V5
0.097
560.2798
54.347141
D1
8.57
V1
0.122
864.4567
105.46372
D2
17.87
V2
0.479
1323.7853
634.09316
D3
15.75
V3
0.537
1170.9607
628.8059
D4
15.41
V4
0.248
1144.988
283.95702
D5
8.31
V5
0.101
661.7477
66.836518
D1
13.88
V1
0.504
1054.9663
531.70302
D2
13.1
V2
0.641
1062.1626
680.84623
D3
12.71
V3
0.313
949.9967
297.34897
D4
6.51
V4
0.137
488.8122
66.967271
5.8451
4.8081
5.0909
5.1987
4
28
M. S. Chauhan et al.
Continued
7
8
9
10
11
12
M-7
M-8
M-9
M-10
M-11
M-12
281
312
307
392
422
559
D1
11.5
V1
0.744
944.3512
702.59729
D2
9.41
V2
0.75
707.7555
530.81663
D3
8.54
V3
0.356
628.8874
223.88391
D4
4.61
V4
0.111
252.4331
28.020074
D1
8.4
V1
0.656
728.3134
477.77359
D2
10.27
V2
0.896
765.2419
685.65674
D3
5.95
V3
0.344
443.2548
152.47965
D4
2.9
V4
0.068
222.3736
15.121405
D1
9.05
V1
0.899
678.7563
610.20191
D2
6.47
V2
0.873
479.2026
418.34387
D3
3.46
V3
0.684
255.54
174.78936
D4
2.25
V4
0.506
169.8287
85.933322
D5
1.45
V5
0.329
5.3285
1.7530765
D1
10.1
V1
0.678
761.6668
516.41009
D2
6.02
V2
0.798
447.5982
357.18336
D3
4
V3
0.776
346.3682
268.78172
D4
3.105
V4
0.581
228.551
132.78813
D5
1.9
V5
0.412
142.8722
58.863346
D6
1.12
V6
0.279
12.7513
3.5576127
D1
4.56
V1
0.671
337.0713
226.17484
D2
4.66
V2
0.771
346.8669
267.43438
D3
5.57
V3
0.835
414.4396
346.05707
D4
4.4
V4
0.797
328.4041
261.73807
D5
3.51
V5
0.571
259.5272
148.19003
D6
1.88
V6
0.461
78.0174
35.966021
D1
4.19
V1
0.817
311.7137
254.67009
D2
4.45
V2
0.79
330.417
261.02943
D3
4.21
V3
0.8
313.0432
250.43456
D4
4.55
V4
0.771
338.2732
260.80864
D5
3.5
V5
0.704
257.2048
181.07218
D6
2.66
V6
0.666
196.848
131.10077
D7
1.81
V7
0.494
135.492
66.933048
D8
1.2
V8
0.253
37.3966
9.4613398
3.7845
4.202
4.1347
5.2795
5.6835
7.5286
29
M. S. Chauhan et al.
Continued
13
14
M-13
M-14
814
694
10.963
D1
3.74
V1
0.524
279.8455
146.63904
D2
4.48
V2
0.56
332.7477
186.33871
D3
5.92
V3
0.526
436.2374
229.46087
D4
6.12
V4
0.516
453.295
233.90022
D5
4.48
V5
0.521
333.9429
173.98425
D6
3.48
V6
0.497
255.3419
126.90492
D7
2.27
V7
0.484
170.2859
82.418376
D8
1.84
V8
0.534
135.8387
72.537866
D9
2.2
V9
0.436
163.9797
71.495149
D10
2.42
V10
0.356
179.3759
63.85782
D11
2.38
V11
0.314
152.1876
47.786906
D1
7.82
V1
0.287
594.5108
170.6246
D2
7.566
V2
0.319
560.7728
178.88652
D3
5.27
V3
0.337
392.2132
132.17585
D4
3.71
V4
0.357
274.2688
97.913962
D5
3.95
V5
0.354
291.6898
103.25819
D6
4.14
V6
0.46
307.0175
141.22805
D7
5.21
V7
0.459
386.965
177.61694
D8
5.72
V8
0.455
424.994
193.37227
D9
5.48
V9
0.43
410.8616
176.67049
D10
4.5
V10
0.39
102.7781
40.083459
9.3468
R.L.
100
90
80
0
50
100
150
200
250
300
Distance from bank (m)
Figure 2. Typical behavior of river cross section w.r.t. Reduced Level (R.L.) at M-1.
30
350
400
450
500
M. S. Chauhan et al.
average depth from D1 to D5 and the area from A1 to A5, M-4 has been divided into 5 parts having the average
velocity from V1 to V5, average depth from D1 to D5 and the area from A1 to A5, M-5 has been divided into 5
parts having the average velocity from V1 to V5, average depth from D1 to D5 and the area from A1 to A5, M-6
has been divided into 4 parts having the average velocity from V1 to V4, average depth from D1 to D4 and the
area from A1 to A4, M-8 has been divided into 4 parts having the average velocity from V1 to V4,average depth
from D1 to D4 and the area from A1 to A4, M-9 has been divided into 5 parts having the average velocity from
V1 to V5, average depth from D1 to D5 and the area from A1 to A5, M-10 has been divided into 6 parts having
the average velocity from V1 to V6,average depth from D1 to D6 and the area from A1 to A6, M-11 has been
divided into 6 parts having the average velocity from V1 to V6,average depth from D1 to D6 and the area from
A1 to A6, M-12 has been divided into 8 parts having the average velocity from V1 to V8, average depth from
D1 to D8 and the area from A1 to A8, M-13 has been divided into 11 parts having the average velocity from V1
to V11, average depth from D1 to D11 and the area from A1 to A11, M-14 has been divided into 10 parts having
the average velocity from V1 to V10, average depth from D1 to D10 and the area from A1 to A10.
4. Data Analysis and Modeling
a) Data Analysis
Before the development of the models of regression, it is the most important to check whether the variables in
data have any correlation or not. Therefore, each cross-sectional data of discharge, depth and velocity are
checked for the multiple regression, the R2, Adjusted R2, Standard error of estimates, standard error, t value and
p value for each cross-section are listed in Table 2 which shows there is a strong correlation between discharge,
depth and velocity data, this analysis gives an clear idea to develop a multiple linear regression model.
R-squared (R2) is a statistical measure of how close the data are to the fitted regression line. It is also known
as the coefficient of determination, or the coefficient of multiple determinations for multiple regressions. The
value (R2) should always between 0% and 100%:
 0% indicates that the model explains none of the variability of the response data around its mean.
 100% indicates that the model explains all the variability of the response data around its mean.
For any regression model first indicator of generalizability is the adjusted (R2) value, which is adjusted for the
number of variables included in the regression equation. This is used to estimate the expected shrinkage in (R2)
that would not generalize to the variable because our solution is over-fitted to the data set by including too many
independent variables. If the adjusted (R2) value is much lower than the (R2) value, it is an indication that our
regression equation may be over-fitted to the sample, and of limited generalizability.
The R2 method is a useful linear regression tool for exploratory model building as it assists in finding subsets
of independent variables that best predict a dependent variable in a given sample (SAS Institute, Inc., 1994).
This algorithm examines all of the possible combinations of the independent variables and ranks them according
to decreasing order of R2 (fraction of the variance explained by the regression) magnitude for the given sample.
Using this output of ranked R2, the best combination of independent variables was selected for further testing for
inclusion in the final regression equations. The type of regression equation that is most suitable to describe the
relation depends naturally on the variables considered and with respect to hydrology on the physics of the
processes driving the variables. Furthermore, it also depends on the range of the data one is interested in.
b) Development of Regression Models
(i) Multiple Regression model for 8 Cross-Sections: For development of the regression model, the complete
data set of all cross-section were analyzed separately. Three cross-sections from both ends of the bend and two
cross-sections from center location have been selected for model development (as shown in Figure 3). Selected
cross-section gives a complete picture of the Varanasi bend of River Ganga. For calibration of the regression
model complete 55 data (about 65% of total) and remaining 31 data (about 35% of total) are used for the validation of the model. As shown in the Table 3 the value of R2 is 0.8674 of the calibrated model which shown a
strong correlation between discharge, depth and velocity data of the complete data set.
Thus developed discharge equation from regression analysis is Q = Yo + a × V + b × D, where Q is Discharge
V is Velocity and D is depth, Yo, a and b are constants which has to determined by regression analysis.
(ii) Partial regression model: For analyzing the fact that whether the discharge is more dependent on which
parameter, depth or velocity, a partial regression model has been studied by keeping depth and velocity constant.
For the modeling purpose (keeping depth constant) the data had shorted in a manner that the depth ranging in
31
M. S. Chauhan et al.
Table 2. Cross-sectional data analysis.
Sr. No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
C-S
M-1
M-2
M-3
M-4
M-5
M-6
M-7
M-8
M-9
M-10
M-11
M-12
M-13
M-14
R
0.9892
0.9973
0.999
0.995
0.9974
0.9997
0.9785
0.9994
0.9998
0.9976
0.999
0.9992
0.9988
0.9201
R2
AdjR2
0.9784
0.9677
0.9946
0.991
0.9981
0.9961
0.9901
0.9802
0.9948
0.9896
0.9993
0.9979
0.9576
0.8727
0.9988
0.9964
0.9997
0.9994
0.9953
0.9921
0.9979
0.9965
0.9984
0.9978
0.9976
0.9969
0.8465
0.8026
Yo
a
−140.1343
−106.0717
−232.0105
−187.1077
−128.5444
−121.947
−261.565
275.978
−126.307
−132.187
−203.784
−87.7579
−103.664
−159.944
2
823.845
1451.219
1086.547
892.8937
b
14.8447
−2.2241
16.5426
17.3317
1178.466
9.0698
1170.01
4.4053
587.393
2038.62
40.15
−137.83
78.1056
73.449
258.619
46.329
306.824
50.422
53.9182
69.184
202.286
37.935
244.71
28.683
2
SEE
28.9603
16.7843
8.4102
28.7211
27.8852
12.27
106.93
18.05
6.3376
17.09
6.3165
4.6753
3.7203
17.493
2
t
P
−4.72
0.01
Std Error
29.66
5.87
0.00
140.24
5.51
0.01
2.69
−3.37
0.04
31.52
202.95
7.15
0.01
−0.33
0.76
6.72
−12.73
0.01
18.22
139.79
7.77
0.02
8.06
0.02
2.05
−3.45
0.07
54.18
9.54
0.01
93.58
3.46
0.07
5.01
−2.38
0.14
54.09
8.24
0.01
142.98
1.40
0.30
6.50
−4.41
0.14
27.67
20.82
0.03
56.20
1.21
0.44
3.65
−1.03
0.49
253.87
1.23
0.44
479.24
0.77
0.58
51.99
2.84
0.22
97.24
6.18
0.10
329.67
−3.69
0.17
37.36
−10.03
0.01
12.59
2.31
0.15
33.87
28.23
0.00
2.60
−5.64
0.01
23.44
5.26
0.01
49.13
14.97
0.00
3.09
−12.53
0.00
16.27
5.72
0.01
53.61
8.21
0.00
6.14
−12.60
<0.0001
6.96
2.00
0.10
26.95
16.86
<0.0001
4.10
−14.09
<0.0001
7.36
11.52
<0.0001
17.55
41.81
<0.0001
0.91
−2.86
0.02
55.97
2.36
0.05
103.59
6.19
0.00
4.63
C-S: cross-section; R: Correlation constant; R : square of the correlation constant; Adj R : adjusted value of R , Yo, a and b are the intercept constants;
SEE: Standard error of estimate, t: test value for each constants; p: test value for each constants and Std Error: standard error for each constants.
32
M. S. Chauhan et al.
Figure 3. Bifurcation of cross-sections at Varanasi Bend of River Ganga.
Table 3. Statistical parameters of the calibrated model.
Profile
8-C-S
R
0.934
Rsqr
0.8723
AdjRsqr
0.8674
Yo
a
−205.169
519.233
b
27.3198
SEE
59.0513
t
P
Std Error
−8.5517
<0.0001
23.9917
13.1601
<0.0001
39.4551
16.096
<0.0001
1.6973
1 m - 5 m, 5 m - 10 m, 13 m - 15 m and finally 15 m - 20 m, the model gives the R2 value as follows 0.816,
0.802, 0.947 and 0.966 respectively. For the model (keeping velocity constant) average the velocity in previously shorted data, it ranged up to 0.3168 m/s, 0.3645 m/s and 0.5 m/s, the model gives the R2 value as follows
0.897, 0.998 and 0.988 respectively as listed in Table 4 below. These values concluded that the discharge is
more depending upon the depth of the flow as the R2 value for the model when velocity is constant is more except once i.e. 0.897.
c) Validation of Model
From whole data set remaining 31 data used for the validation of the model. The detailed calculation for each
data is shown in Table 5. From this it is clearly noticeable that at very low discharge values, depth below 5 m
and low velocities, the model doesn’t works properly and it gives unreasoned results.
5. Result and Discussion
River hydraulics is quite complex in natural channels and rivers. For practical and engineering purposes, the
flows in river channel are often characterized by depth averaged or cross-sectional averaged properties. While
these simplifications might be justifiable and necessary for practical reasons, it is important to be cognizant
about the complex nature of the three-dimensional free-surface flows in rivers and open channels. A better understanding of the hydraulic properties in natural rivers would give rise to a more accurate approximation in
practical applications. In this study, the velocity distribution in a river cross-section has been investigated in detail.
Also as we know that atmospheric and human intervention affects the hydrology of any area which influences
the flow behavior of river. To understand these effects on main governing parameters of hydraulics on river flow
characteristics, 14 different cross section shad marked along the river which lies between 7500 m. The river flow
velocity, width and depth has been computed and plotted to compare each other and identified their relationship
among the above said parameters. The results showed that river depth is almost having increasing trend except
the cross section (M-2), second last from downstream as clearly shown in Figure 4(a).
33
M. S. Chauhan et al.
Table 4. Statistical parameters of the partial regression model.
Sr. No.
R²
Std. deviation
MSE
RMSE
Yo
A
Range
1
0.816
36.261
1205.293
34.717
−44.442
342.204
1-5m
2
0.802
59.932
3169.251
56.296
−35.172
633.193
5 - 10 m
3
0.947
53.104
2115.015
45.989
62.655
769.011
10 - 15 m
4
0.966
11.597
89.657
9.469
150.237
805.866
15 - 20 m
5
0.897
45.307
1824.616
42.716
−60.380
22.605
0.3168 m/s
6
0.998
5.656
25.593
5.059
1.750
25.202
0.3645 m/s
7
0.988
17.128
234.689
15.320
19.174
28.876
0.5 m/s
Constant Parameter
Depth
Velocity
Table 5. Discharge data for validation of model.
Sr. No.
Velocity
Depth
Observed Discharge
A × Velocity
B × Depth
Modeled discharge
% error
1
0.173
15.1
219.9486189
89.827309
412.529
297.186989
35.11655
2
0.489
16.31
588.9922848
253.904937
445.5859
494.321575
−16.0733
3
0.507
12.52
472.2879408
263.251131
342.0439
400.125727
−15.2793
4
0.295
11.06
242.3925615
153.173735
302.157
250.161423
3.205074
5
0.097
7.62
54.3471406
50.365601
208.1769
53.373177
−1.79212
6
0.122
8.57
105.4637174
63.346426
234.1307
92.307812
−12.4743
7
0.479
17.87
634.0931587
248.712607
488.2048
531.748133
−16.1404
8
0.537
15.75
628.8058959
278.828121
430.2869
503.945671
−19.8567
9
0.248
15.41
283.957024
128.769784
420.9981
344.598602
21.3559
10
0.101
8.31
66.8365177
52.442533
227.0275
74.300771
11.16793
11
0.504
13.88
531.7030152
261.693432
379.1988
435.722956
−18.0514
12
0.641
13.1
680.8462266
332.828353
357.8894
485.548433
−28.6846
13
0.313
12.71
297.3489671
162.519929
347.2347
304.585287
2.433612
14
0.137
6.51
66.9672714
71.134921
177.8519
43.817519
−34.5688
15
0.899
9.05
610.2019137
466.790467
247.2442
508.865357
−16.6071
16
0.873
6.47
418.3438698
453.290409
176.7591
424.880215
1.562434
17
0.684
3.46
174.78936
355.155372
94.52651
244.51258
39.88985
18
0.506
2.25
85.9333222
262.731898
61.46955
119.032148
38.51687
19
0.329
1.45
1.7530765
170.827657
39.61371
5.272067
200.7323
20
0.678
10.1
516.4100904
352.039974
275.93
422.800654
−18.127
21
0.798
6.02
357.1833636
414.347934
164.4652
373.64383
4.608408
22
0.776
4
268.7817232
402.924808
109.2792
307.034708
14.23199
23
0.581
3.105
132.788131
301.674373
84.82798
181.333052
36.55818
24
0.412
1.9
58.8633464
213.923996
51.90762
60.662316
3.05618
25
0.279
1.12
3.5576127
144.866007
30.59818
−29.705117
−934.973
26
0.671
4.56
226.1748423
348.405343
124.5783
267.814331
18.41031
27
0.771
4.66
267.4343799
400.328643
127.3103
322.469611
20.57897
28
0.835
5.57
346.057066
433.559555
152.1713
380.561541
9.970747
29
0.797
4.4
261.7380677
413.828701
120.2071
328.866521
25.64719
30
0.571
3.51
148.1900312
296.482043
95.8925
187.205241
26.32782
31
0.461
1.88
35.9660214
239.366413
51.36122
85.558337
137.8866
34
M. S. Chauhan et al.
16
14
Depth (m)
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
10
11
12
13
14
15
10
11
12
13
14
15
10
11
12
13
14
Cross Section ( U/s to D/s )
(a)
900
800
width (m)
700
600
500
400
300
200
100
0
0
1
2
3
4
6
5
7
8
9
Cross Section ( U/s to D/s )
(b)
0.8
0.7
Velocity (m/s)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
Cross Section ( U/s to D/s )
(c)
900
800
700
width (m)
600
500
400
300
200
100
0
0
1
2
3
4
5
6
7
8
Cross Section ( U/s to D/s )
9
15
(d)
Figure 4. (a) Depth Variation along with cross section from M-14 to M-1; (b) Width variation with cross section from M-14
to M-1; (c) Velocity distribution with cross section from M-14 to M-1; (d) Discharge variation with cross section from M-14
to M-1.
35
M. S. Chauhan et al.
Leaving the starting upstream station (M-14) the width of river is almost having decreasing trend till (M-6)
cross section as shown in Figure 4(b). This shows a varying average depth and average width of flow at its different cross section due to its meandering and sinusoidal characteristics.
Generally long profile gradient of river is decreases in downstream due to increasing hydraulic radius (cross
section efficiency) but here at Varanasi bend the velocity is increasing up to M-12 cross section after which the
inconsistent bend for velocity obtained although from the M-7 cross section the average velocity of flow is continuously decreasing as shown in Figure 4(c). The above theory of increasing velocity in downstream seems to
be not valid for River Ganga at Varanasi bend. The decreasing of velocity had resulted by the increasing the
depth of flow in downstream consistency. Discharge variation with the cross sections is also shown in Figure
4(d).
Any stream with having changing volume may assume a meandering course, alternatively eroding sediments
from the outside of a bend and depositing them on the inside. This meandering characteristic and sinuosity along
Ganga river course had showed non uniformity in the river width and uneven depth of water. The main cause of
overall these parameters is heavy rainfall from which the runoff in term of river flow depends. The rainfall intensity mainly governs the amount of erosion and the geological parameters decide the deposition of eroded sediment in the river which leads to variation in the geometry of any river. Human activity is also the indisputable
cause for high flow which involved of building of impervious structures, deforestation, and caused to the higher
surface runoff and decrease the time of concentration by which even on small rainfall leads to change in depth of
river flow. On the other hand, forestation such as pine tree and other tree which can increase infiltration so that
time of peak can delay and its harmful effects can be reduced. To minimize the impact of surface runoff directly
to the river flood mitigations concept should be undertaken and another river training work to be adopted along
the Ganga River in order to minimize erosion as well as sedimentation enter to the river.
6. Conclusions
The monitoring of discharge and velocity distribution was conducted using consistent protocols designed to ensure the scientific validity of the data. These stream flow datasets will aid in the management of water resources
in a sustainable manner for the benefit of water users and the environment.
A multiple linear regression model was developed by using the measured discharge, depth and velocity
through ADCP of Varanasi bend of river Ganga. The regression equation shows a high correlation between the
discharge, depth and velocity parameters with the R2 value of 0.8624. Among the validation set of 31 data’s, 9
data’s of discharge were in the range of 100m3/s and out of which 6 data’s gave more errors, as well as the average velocity lies in the range of 0.101 m/s to 0.279 m/s in validation set which gave more errors in validation
of model. The proposed model is validated for the average velocity greater than 0.279 m/s up to 0.899 m/s. The
developed model also shows variation when the depth of flow is less than 5 m, so this model is suitable for the
depth above 5 m up to the maximum of 19.98 m at the Varanasi bend of River Ganga. The equations developed
for this study are not applicable for ungaged sites in which the basin characteristics are not in the range of those
used to develop the regression equations.
Acknowledgements
Authors are thankful to Department of Civil Engineering, Indian Institute of technology (BHU) for providing the
infrastructure and computational facilities to complete this work.
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